Amplitude Modulation of Complex Exponential Carrier-Signals And Systems-Lecture Slides, Slides of Signals and Systems Theory

Download Amplitude Modulation of Complex Exponential Carrier-Signals And Systems-Lecture Slides and more Slides Signals and Systems Theory in PDF only on Docsity! 2 3 Amplitude Modulation (AM) of a Complex Exponential Carrier c t( ) = ej! c t , !c —carrier frequency y(t) = x(t) e j! ct = X j ! "!c( )( ) Y j!( ) = 1 2" X j!( )#C j!( ) = 1 2! X j"( )# 2!$ " %" c( ) 4 Demodulation of Complex Exponential AM Corresponds to two separate modulation channels (quadratures) with carriers 90o out of phase e j!c t = cos!ct + j sin!ct " docsity.com 3 5 Sinusoidal AM Drawn assume ωc > ωM Y j!( ) = 1 2" X j!( )# " $ ! %!c( ) + $ ! +!c( ){ } x(t) y(t) = x(t)cosωct cosωct × = 1 2 X j ! "! c( )( ) + 1 2 X j ! +!c( )( ) 6 Synchronous Demodulation of Sinusoidal AM Suppose θ = 0 for now, ⇒ Local oscillator is synchronized with the carrier. Implemented in practice by using phase- locked loops (PLL). of the local oscillator docsity.com 6 11 Double-Sideband (DSB) and Single-Sideband (SSB) AM DSB, occupies 2 ωM bandwidth in ω > 0, even though all the information is contained in ωM. Each only occupies ωM bandwidth in ω > 0. USB LSB Since x(t) and y(t) are real, from conjugate symmetry, both LSB and USB signals carry exactly the same information. 12 Single Sideband Modulation Can also get SSB/SC or SSB/WC docsity.com 7 13 Frequency-Division Multiplexing (FDM) (Examples: All the radio-station signals and analog cell phones) All the channels can share the same physical medium. air 14 FDM in the Frequency-Domain Channel a Channel b Channel c Multiplexed signals docsity.com 8 15 Demultiplexing and Demodulation • Channels must not overlap ⇒ Bandwidth Allocation. • It is difficult (and expensive) to design a highly selective bandpass filter with a tunable center frequency (the SAW bandpass filters are fixed). • Solution — the Superheterodyne Receivers. ωa needs to be tunable 16 The Superheterodyne Receiver (used in all radios) Operation principle: — Down convert from ωc to ωIF, and use a coarse tunable BPF for the front end to block the image signals at ωI = ωLO+ ωIF. — Use a sharp-cutoff fixed BPF at ωIF to get rid of other signals. AM, ! c 2" = 535 #1605 kHz — RF FCC: ! IF 2" = 455 kHz — IF ωLO+ ωIF docsity.com